First Stretch then Shrink and Bulk: A Two Phase Approach for Enumeration of Maximal (Δ, γ)Cliques of a Temporal Network
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A Temporal Network (also known as Link Stream or Time-Varying Graph) is often used to model a time-varying relationship among a group of agents. It is typically represented as a collection of triplets of the form (u,v,t) that denotes the interaction between the agents u and v at time t. For analyzing the contact patterns of the agents forming a temporal network, recently the notion of classical clique of a static graph has been generalized as ΔClique of a Temporal Network. In the same direction, one of our previous studies introduces the notion of (Δ, γ)Clique, which is basically a vertex set, time interval pair, in which every pair of the clique vertices are linked at least γ times in every Δ duration of the time interval. In this paper, we propose a different methodology for enumerating all the maximal (Δ, γ)Cliques of a given temporal network. The proposed methodology is broadly divided into two phases. In the first phase, each temporal link is processed for constructing (Δ, γ)Clique(s) with maximum duration. In the second phase, these initial cliques are expanded by vertex addition to form the maximal cliques. From the experimentation carried out on 5 realworld temporal network datasets, we observe that the proposed methodology enumerates all the maximal (Δ,γ)Cliques efficiently, particularly when the dataset is sparse. As a special case (γ=1), the proposed methodology is also able to enumerate (Δ,1) ≡Δcliques with much less time compared to the existing methods.
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